Question

choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x − 2y = 6 2x y = 5 −4x − 2y = 10 −4y = 4 −4x − 5y = −1 −7y = 5 3x 2y = 6 7x = 12 4x 2y = 10 8x = 16 -------------------------------------------------------------------------------- question 2 solve the following system of equations: x − 2y = 14 x 3y = 9 (1, 12) (−1, −12) (12, −1) (12, 1) -------------------------------------------------------------------------------- question 3 (multiply) determine which system below will produce infinitely many solutions. −6x 3y = 18 4x − 3y = 6 2x 4y = 24 6x 12y = 36 3x − y = 14 −9x 3y = −42 5x 2y = 13 −x 4y = −6 -------------------------------------------------------------------------------- question 4 solve the following system of equations: x − 2y = 14 x 3y = 9 (1, 12) (−1, −12) (12, −1) (12, 1) -------------------------------------------------------------------------------- question 5 solve the system of equations. x 3y = −1 2x 2y = 6 (−4, 1) (2, −1) (4, −1) (5, −2) -------------------------------------------------------------------------------- question 6 if you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution to the system? the solution is (1, 3) the solution is x = 1 and y = 3 there is no solution there are infinitely many solutions -------------------------------------------------------------------------------- question 7 the art museum had a total of 224 visitors on tuesday. visitors older than 18 paid $12 for admission. visitors 18 years or younger paid $8 for admission. the museum collected a total of $2,520. how many visitors were 18 or younger? 42 56 182 194 -------------------------------------------------------------------------------- question 8 solve the system of equations by substitution. what is the solution for x? 2x y = 1 4x 2y = −1 x = 0 x = 2 there is no x value, as there is no solution. x can be any value, as there is an infinite number of solutions.

Answer 1

#1. The answer is D. 4x + 2y = 10
                                  8x = 16

#3. The answer is C. 3x − y = 14                                                          
                              −9x + 3y = −42

#6. The answer is C. There is no solution.

#8. The answer is C. There is no x value, as there is no solution.

Answer 2

4x − 2y = 6 . . . . . (1)
2x + y = 5 . . . . . (2)

(2) x 2 => 4x + 2y = 10 . . . . . (3)

(1) - (3) gives: -4y = -4
y = -4/-4 = 1

From (2), 2x + 1 = 5 => 2x = 5 -1 = 4
x = 4/2 = 2

Solution is (2, 1)

Substituting the solution into the options gives that
−4x − 2y = 10
−4y = 4 −4x
has the same solution.